Cannot save object renderability in a scene?
The objects in scene "5.2" won't let you change their options because the whole scene which they are part of is linked. This can be detected by small white sign with an arrow just next to the linked object or any datablock:



It's all about the linking data in Blender. The library is a .blend file located somewhere else (but Blender knows where it is as it can read the data from that file) where that data is stored. To edit those objects you can either:


edit those objects only from the file they were created in.
make a local copy of the objects.


The first way assumes you will continously switch between the different .blend files - change some options in the main .blend (where the object / group / some other useful data is stored), then return back to .blend where objects are imported to (e.g. for rendering), change their locations, etc., etc.
However the structure will be organized - all the data will be stored in its own files and only uneditable entities will be stored in the working file (which is sometimes preferred).
This may be possible with using some addons, like Edit Linked Library and so on. For more info refer to How can I modify the mesh of a linked character?

The second way will let you edit any mesh or object, change it properties, edit everything about it - but full editable copies of these objects will be present in every file, with all the consequences (every file will occupy much more space; meshes might get changes assumed for one project which is undesired for another project etc).
See Change linked object to appended? and Kind of &quot;soft link&quot; of objects between scenes?